Illustrated Physics
physics, drawn
Concept

Destructive interference — where it appears

The cancellation that occurs where two waves meet out of step, crest against trough, so that their amplitudes subtract. The energy is not destroyed but redistributed to places of constructive interference, which is why anti-noise silences only a region and not a whole room.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

What a real coating leaves behind, and over what range. Reflectance against wavelength for a glass surface of index 1.52 in air, uncoated and with quarter-wave layers of 2 different indices, each a quarter of a wave thick at 550 nm. The ideal index is the geometric mean, 1.2329, and the layer made of it takes the reflectance to zero at the design wavelength exactly. No durable solid has that index: magnesium fluoride at 1.38 is the usual compromise and it leaves 1.26% at the design wavelength against 4.26% bare — a reduction of 3.4× rather than a removal. Both curves rise away from the design wavelength, because the thickness is a quarter of a wave only there, and the useful band is wide but not unlimited: the better coating stays under a quarter of the bare reflectance from 415 to 780 nm. The purple cast of a coated lens is that residual — the ends of the visible reflecting while the middle does not.

The layer that makes a reflection vanish

A wave meeting a step in impedance reflects, and nothing can be done about the step. Put a third medium between the two, a quarter of a wavelength thick and of exactly the intermediate impedance, and the reflection stops existing — not reduced, cancelled.

waves · Impedance Where cancelling a 500 Hz tone works. Sound at 500 Hz (wavelength 69 cm) arriving from every direction at random, as it does in a room or a cabin, and a small loudspeaker 50 cm to the left of a microphone (black dot), driven to cancel the sound exactly at the microphone. Contours mark where the sum is 20 dB quieter than the original (red), 10 dB quieter (blue), unchanged (grey) and 6 dB louder (black), in a plane through both. The zone at least 10 dB quieter is 12.0 cm across, at right angles to the line from speaker to microphone — 0.18 of a wavelength — and beyond the unchanged contour the cancelling source only adds sound. Silence has been made at a point, not in a room.

The silence that fits in a tenth of a wavelength

Two sounds of equal strength and opposite phase add to nothing, so any noise can be cancelled by playing its inverse. At one point. A microphone and a loudspeaker can silence the air exactly where the microphone is, and nowhere else for certain: in the diffuse sound of a room the quiet zone is a few tenths of a wavelength across, under ten centimetres at a kilohertz, and beyond it the cancelling speaker only adds noise. That is why noise cancellation works in a headphone and not in a room, and why it works on the drone of an engine and not on a voice.

waves · Superposition

Named alongside it

The objects these essays reach for when they reach for this one.

Acoustic impedanceActive noise controlAntireflectionBandwidthBragg mirrorCausalityDiffuse fieldGeometric meanImpedanceInterferenceMonopoleQuarter-wave

All concepts